A165815 -id:A165815 - cp's OEIS frontend

A165816 Prime congruent numbers (A165815) that are not equal to 5 or 7 (mod 8).

41, 137, 257, 313, 353, 457, 761, 1201, 1217, 1249, 1321, 2113, 2273, 2777, 2833, 2953, 3001, 3433, 3593, 3761, 3881, 4441, 4481, 4649, 4793, 4889, 5273, 5449, 5569, 5657, 5849, 6073, 6529, 7001, 7321, 7417, 7561, 7793, 8521, 8609, 9049, 9257, 9281

Offset: 1

T. D. Noe, Sep 28 2009

nonn

Heegner proved that every prime p with p = 5 or 7 (mod 8) is a congruent number. See A003628 for those primes. All primes in this sequence equal 1 (mod 8).

Monsky proved that no prime of the form 8k+3 is a congruent number. - Jonathan Sondow, Nov 15 2017

T. D. Noe, Primes less than 10^7
Kurt Heegner, Diophantische Analysis und Modulfunktionen, Math. Zeitschrift 56 (1952), 227-253.
P. Monsky, Mock Heegner points and congruent numbers, Math. Zeit., 204 (1990), 45-67.
Kent E. Morrison, Congruent Numbers

Cf. A003273 (congruent numbers), A165815 (prime congruent numbers).

A337704 Pythagorean primes that are not congruent numbers.

Original entry on oeis.org

17, 73, 89, 97, 113, 193, 233, 241, 281, 337, 401, 409, 433, 449, 521, 569, 577, 593, 601, 617, 641, 673, 769, 809, 857, 881, 929, 937, 953, 977, 1009, 1033, 1049, 1097, 1129, 1153, 1193, 1289, 1297, 1361, 1409, 1433, 1481, 1489, 1553, 1601, 1609, 1657, 1697, 1721, 1753

Offset: 1

Jani Melik, Sep 16 2020

nonn

			17 is a Pythagorean prime and is not congruent because it is not the area of a right triangle with rational sides. So 17 is a term.

Intersection of A002144 and A165564.

Cf. A003273, A269727, A165815.

cp's OEIS Frontend

A165816 Prime congruent numbers (A165815) that are not equal to 5 or 7 (mod 8).

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A337704 Pythagorean primes that are not congruent numbers.

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